Catalysis and Catalysts - Kinetics
Catalytic Reaction KineticsCatalytic Reaction Kinetics
Why catalytic reaction kinetics Derivation rate expressions Simplifications
– Rate determining step– Initial reaction rate
Limiting cases– Temperature dependency– Pressure dependency
Examples
Catalysis and Catalysts - Kinetics
Reactor design equationReactor design equation
dx
d W Fri
ii
stoichiometric coefficient i
catalyst effectiveness
rate expression
conversion i
‘space time’
Catalysis and Catalysts - Kinetics
Simple example: reversible reaction A B
Simple example: reversible reaction A B
A B
A*
B*
‘Elementary processes’
‘Langmuir adsorption’
1
2
3A + * A*
k1
k-1
A* B*k-2
k2
B* B + *k3
k -3
1.
2.
3.
Catalysis and Catalysts - Kinetics
Elementary processesElementary processes
Rate expression follows from rate equation:
At steady state:
1 1 1 1 A T * 1 T Ar r r k p N k N
2 2 2 2 T A 2 T Br r r k N k N
3 3 3 3 T B 3 B T *r r r k N k p N
Eliminate unknown surface occupancies
1 2 3r r r r
Catalysis and Catalysts - Kinetics
Site balance:(7.5)
Steady-state assumption:(7.6-7)
Rate expression:(7.9)
* A B1
A
B
d0
dd
0d
t
t
T 1 2 3 A B eq
eq 1 2 3A B
( / )with:
(.....) (......) (......)
N k k k p p Kr K K K K
p p
Elementary processes contd.Elementary processes contd.
Catalysis and Catalysts - Kinetics
Quasi-equilibrium / rate-determining stepQuasi-equilibrium / rate-determining step
r+1
r +2
r+3
r-1
r-2
r-3
r
rate determining
‘quasi-equilibrium’
r = r+2 - r-2
Catalysis and Catalysts - Kinetics
Rate expression r.d.s.Rate expression r.d.s.
2 2 2 T A 2 T Br r r k N k N
Rate determining step:
Eliminate unknown occupancies
Quasi-equilibrium:
1 1 1 A T * 1 T A r r k p N k N
So:
1A 1 A * 1
1
BB *
3
with: k
K p Kk
p
K
Catalysis and Catalysts - Kinetics
Rate expression, contd.
Substitution:
2 2 2 T 1 A * 2 T B * 3
2 T 1 * A B eq
/
/
r r r k N K p k N p K
r k N K p p K
B
eq 1 2 3A eq
pK K K K
p
where:
Unknown still *
Catalysis and Catalysts - Kinetics
Rate expression, contd.
Site balance:
* A B * 1 A B 31 1 /K p p K
*1 A B 3
1
1 /K p p K
Finally:
T 2 1 A B eq
1 A B 3
/
1 /
N k K p p Kr
K p p K
Catalysis and Catalysts - Kinetics
Adsorption r.d.s
Surface reaction r.d.s.
Desorption r.d.s.
T 2 1 A B eq
1 A B 3
/
1 /
N k K p p Kr
K p p K
T 3 1 2 A B eq
2 1 A
/
1 1
N k K K p p Kr
K K p
T 1 A B eq
2 B 3
/
1 1 1/ /
N k p p Kr
K p K
Other rate-determining stepsOther rate-determining steps
Catalysis and Catalysts - Kinetics
Langmuir adsorptionLangmuir adsorption
Uniform surface (no heterogeneity) Constant number of identical sites Only one molecule per site No interaction between adsorbed species
A + * A*
A AA
A A1
K p
K p
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0.1
100
10
1
pA (bar)
KA (bar-1)
Catalysis and Catalysts - Kinetics
Equilibrium constant
Adsorption constant
Reaction entropy
Reaction enthalpy
Adsorption enthalpy,<0(J/mol)
Adsorption entropy, <0(J/mol K)
atm-1
oooeq STTHTGKRT )()(ln
)(, TGi
oifi
0 0
ln A AA
S HK
R RT
ThermodynamicsThermodynamics
Catalysis and Catalysts - Kinetics
Multicomponent adsorption / inhibitionMulticomponent adsorption / inhibition
Langmuir adsorption
A A
A A I I1A
K p
K p K p
Inhibitors
Catalysis and Catalysts - Kinetics
Dissociative adsorptionDissociative adsorption
H2 + 2* 2H*
2 2
2 2
0.5
H H
H 0.5
H H1
K p
K p
Two adjacent sites needed
Catalysis and Catalysts - Kinetics
Langmuir-Hinshelwood/Hougen-Watson models (LHHW)
Langmuir-Hinshelwood/Hougen-Watson models (LHHW)
rkinetic factor driving force
adsorption term
( ) ( )
( )n
includes NT, k(rds)
For: A+B C+D
pApB-pCpD/Keq
molecular: KApA
dissociative: (KApA)0.5 = 0, 1, 2number of species in r.d.s.
Catalysis and Catalysts - Kinetics
Verwerking p. 11 t/m 13
Catalysis and Catalysts - Kinetics
Initial rate expressionsInitial rate expressions
Forward rates Product terms negligible
0 T 1 A0r N k p T 2 A A0
0A A01
N k K pr
K p0 T 3r N k
r0
T1
T2
T3
pA0pA0 pA0
T1
T2
T3
T1
T2
T3
Adsorption Surface reaction Desorption
(K2 and KApA0 >>1)
Catalysis and Catalysts - Kinetics
Ethanol dehydrogenationEthanol dehydrogenationFranckaerts &Froment
C2H5OH CH3CHO + H2
Model:
1. A + * A*2. A* + * R* + S* (r.d.s.)3. R* R + *4. S* S + *
= Derive rate expression =
Cu-Co cat.
Catalysis and Catalysts - Kinetics
Initial rates - linear transformationInitial rates - linear transformation
Full expression
Initial rate
After rearrangement
2 T A A R S eq
2
A A R R S S
/K
1
k s N K p p pr
K p K p K p
A A
0 2 T2
A A
with1
k K pr k k sN
K p
A AA
0 A A
1p Kp
r k K k K
y a b x linear form:
linear least squares fittrends, positive parameters
Ethanol dehydrogenation
Catalysis and Catalysts - Kinetics
Initial rates - CO hydrogenation over RhInitial rates - CO hydrogenation over RhVan Santen et al.
Kinetic model
1. CO + * CO*2. CO* + * C* + O* (r.d.s.)
0 T 2 CO *r sN k
2 T CO CO
0 2
CO CO1
sk N K pr
K p
Initial rate
0.2
0.4
0.6
0.8
1.0
Occupancy (-) 400450
500550
600
Temperature (K)
0
200
400
600
800
Ra
te
Catalysis and Catalysts - Kinetics
*A *A# *Bk-#
k+# kbarrier
Verwerking p. 18 t/m21
Temperature and Pressure DependenceTemperature and Pressure Dependence
Catalysis and Catalysts - Kinetics
Limiting cases - forward ratesLimiting cases - forward rates
Surface reaction r.d.s.
2 T A A
A A B B1
k N K pr
K p K p
1. Strong adsorption A
2 Tr k N
obsa a2E E
A*
B*
A* #
Ea2
Catalysis and Catalysts - Kinetics
2. Weak adsorption
2 T A Ar k N K p
obsa a2 AE E H
Surface reaction r.d.s.
2 T A A
A A B B1
k N K pr
K p K p
A*
A(g) + *
A* #
Ea2
HA
Limiting cases - forward ratesLimiting cases - forward rates
Catalysis and Catalysts - Kinetics
3. Strong adsorption B
2 T A A
B B
k N K pr
K p
obsa a2 A BE E H H
Surface reaction r.d.s.
2 T A A
A A B B1
k N K pr
K p K p
A* #
B* + A
B + *+ AEa2
A*- HB
HA
Limiting cases - forward ratesLimiting cases - forward rates
Catalysis and Catalysts - Kinetics
Cracking of n-alkanes over ZSM-5J. Wei I&EC Res.33(1994)2467
Ea2
Eaobs
HA
Carbon number
kJ/mol
200
100
-200
-100
0
0 2 A Ar k K p
obsa a2 AE E H
Catalysis and Catalysts - Kinetics
Observed temperature behaviourObserved temperature behaviour
1/T
ln robs
desorption r.d.s.
adsorption r.d.s.
•T higher coverage lower•Highest Ea most favoured
Change in r.d.s.
Catalysis and Catalysts - Kinetics
Pt-catalysed dehydrogenation of methylcyclohexane:
M T + H2
Two kinetic significant steps:* + M ....T* T + *
mari
no inhibition by e.g. benzeneT* much higher than equilibrium with gas phase T
‘Kinetic Coupling’ two kinetically significant steps
‘Kinetic Coupling’ two kinetically significant steps
Catalysis and Catalysts - Kinetics
Heat of adsorption
Rate
Sabatier principle - Volcano plotSabatier principle - Volcano plot
Catalysis and Catalysts - Kinetics
Langmuir adsorption– uniform sites– no interaction adsorbed species– constant number of sites
Rate expression– series of elementary steps– steady state assumption – site balance– quasi-equilibrium / rate determining step(s)– initial rates
simpler
mechanism kinetics
SummarySummary
Catalysis and Catalysts - Kinetics
Catalysed N2O decomposition over oxidesWinter, Cimino
Rate expressions:
rk p
p Kobs N O
O
2
21 3
0.5
r k pobs N O 2
r k
p
pobs
N O
O
2
2
0.5
1st order
strong O2 inhibition
moderate inhibition
Also: orders 0.5-1water inhibition
= Explain / derive =
Catalysis and Catalysts - Kinetics
N2O decomposition over Mn2O3
2 N2O 2N2 + O2
Vannice et al. 1995
Rate expression
rk N K p
K p p KT N O
N O O
2 1
1 3
0.52
2 21
Kinetic model
1. N2O + * N2O*2. N2O* N2 + O*3. 2 O* 2* + O2
Catalysis and Catalysts - Kinetics
N2O decomposition over Mn2O3
Vannice et al. 1995
Oxygen inhibitionorder N2O ~0.78
Eaobs= 96 kJ/mol
= Explain =
0.0 2.0 4.0 6.0 8.0 10.0
pO2 / kPa
0.0
0.1
0.2
0.3
0.4
r / 1
0-6
mol
.s-1.g
-1648 K
638 K
623 K608 K
598 K
pN2O = 10 kPa
Catalysis and Catalysts - Kinetics
N2O decomposition over Mn2O3
Vannice et al. 1995
Kinetic model
1. N2O + * N2O*2. N2O* N2 + O*3. 2 O* 2* + O2
Rate expression
5.031
12
22
2
1 KppK
pKNkr
OON
ONT
Values
Ea2 130 kJ / mol
K J/mol 109S
kJ/mol 92
3
3
H
K J/mol 38S
kJ/mol 29
1
1
H
= Thermodynamically consistent =
Catalysis and Catalysts - Kinetics
N2O decomposition over ZSM-5 (Co,Cu,Fe)
2 N2O 2N2 + O2
Kapteijn et al. 11th ICC,1996
Rate expression
rk N p
k kT N O
1
1 2
2
1
Kinetic model
1. N2O + * N2 + O*2. N2O + O* N2 + O2 + *
no oxygen inhibition
Catalysis and Catalysts - Kinetics
N2O decomposition over ZSM-5 (Co,Cu,Fe)Kapteijn et al. 11th ICC,1996
Rate expression
rk N p
k k K pT N O
O
1
1 2 3
2
21
Oxygen inhibition model
1. N2O + * N2 + O*2. N2O + O* N2 + O2 + *3. O2 + * *O2
0 2 4 6 8 10
p(O2 ) / kPa
0.0
0.2
0.4
0.6
0.8
1.0
X(N
2O
)
Fe-ZSM-5
Co-ZSM-5
Cu-ZSM-5
743 K
833 K
793 K
733 K
773 K
688K
Catalysis and Catalysts - Kinetics
Effect of CO on N2O decomposition
0.0 0.5 1.0 1.5 2.0
molar CO/N2O ratio
0.0
0.2
0.4
0.6
0.8
1.0
X(N
2O
)
Co-ZSM-5 (693 K)
Cu-ZSM-5 (673 K)
Fe-ZSM-5 (673 K)
CO removes oxygen from surfaceso ‘enhances’ step 2, oxygen removal
now observed: rate of step 1 r1 = k1 NT pN2O
increase: ~2, >3, >100
CO + O* CO2 + *
CO + * CO* (Cu+)
Catalysis and Catalysts - Kinetics
Effect of CO on N2O decomposition
rate without CO rate with CO
r k N pT N O 1 2
So k1/k2 = : 1 Co>2 Cu>100 Fe
ratio = 1 + k1/k2 and:21
21* 1 kk
kkO
O* 0.7>0.9>0.99
21
1
12
kk
pNkr ONT
Catalysis and Catalysts - Kinetics
Apparent activation energies N2O decompositionCO/ N2O = 2
Cu rk N p
k k K p
k N p
K pT N O
CO CO
T N O
CO CO
1
1 2
12 2
1
Co, Fe
r k N pT N O 1 2
E Eaobs
a 1
E E Haobs
a CO 1
Apparent activation energies (kJ/mol)
only N2O CO/N2O=2
Co 110 115
Cu 138 187
Fe 165 78
Catalysis and Catalysts - Kinetics
Apparent activation energies N2O decompositionCO/ N2O = 0
Co,Cu
Fe
rk N p
k kT N O
1
1 2
2
1
r k N pT N O 2 2 E Eaobs
a 2
E E Eaobs
a amix( )1 2,
Apparent activation energies (kJ/mol)
only N2O CO/N2O=2
Co 110 115
Cu 138 187
Fe 165 78
Catalysis and Catalysts - Kinetics
Complex kineticsHDN of Quinone over NiMo/Al2O3 (Prins & Jian, Zurich)
Kinetic scheme
Q THQ1 OPA PB
THQ5 DHQ PCHA
PCH
PCHE
N N
NN
NH2
NH2
Purpose: Kinetics of reactionEffects functions Ni and MoAddition role of P
Catalysis and Catalysts - Kinetics
Complex kinetics
Subscheme research: HDN of OPA
OPA PB
PCHA PCHPCHE
NH2
NH2
Not observedintermediate,not significant
Catalysis and Catalysts - Kinetics
Complex kineticsHDN of OPA
Derived global scheme:
OPA PB
PCHPCHE
k3
k5
k6
k1
NH2 How can this ‘direct’ stepbe rationalised?
Catalysis and Catalysts - Kinetics
Complex kineticsHDN of OPA (Jiang & Prins)
Reaction modelling
space time (cs)
0 10 20 30 40 50 60
0.0
0.2
0.4
0.6
0.8
1.0
0
1
2
3
4
5
OPA NiMo one site model 370C
Par
tial p
ress
ure
(kP
a)
Par
tial p
ress
ure
(kP
a)
OPA
PBPCHE
PCH
strong adsorptionN-containg species
plug flow reactor
excellent fit
Catalysis and Catalysts - Kinetics
Complex kineticsHDN of OPA
OPA + *
OPA* PB + *
PCHA* PCHA + *
PCHE* PCHE + *
PCH + *
HCs not adsorbed(weakly compared to N-s)
Only traces foundFast reactionsteps
slow
The direct route to PCH
Competitive parallel steps
Other hydrogenation functional sites ?
Direct globalroutes
kb
ka
kc
kd ke
Catalysis and Catalysts - Kinetics
Rate expressions•Steady state assumption•Site balance (one site)•Strong adsorption N-species
r
k k K p
kk k
K p K pOPA
a b OPA OPA
a
c dOPA OPA NH NH
1 1
3 3
r
k kk k
K p k p
kk k
K p K pPCH
a d
a dOPA OPA e PCHE
a
c dOPA OPA NH NH
1 1
3 3
parallel reactions
direct routefrom PCHE
Q: explain zero order OPA
Catalysis and Catalysts - Kinetics
Catalysis and Catalysts - Kinetics
‘Kinetic coupling’two steps kinetically significant
Decomposition of ammonia over Mo (low p, high T)
2NH3 -> N2 + 3H2
Steps: 2NH3 + * -> 2N* + 3H2
2N* -> N2
surface concentration N much higher than equilibriumwith N2 pressure
‘fugacity of N* corresponds with virtual fugacity N2
Catalysis and Catalysts - Kinetics
Virtual fugacity, kinetic coupling
Aromatization light alkanes over zeolite
Alkanes -> Aromatics + Hydrogen
• Cracking yields high H*, so high fugacity H*• H* not in equilibrium with H2
-> low aromatics selectivity
Addition of Ga provides escape route for H*
Kinetic coupling used to increase reaction selectivity for aromatics
zeolite: alkane -> 2H* + .....Ga: 2H* -> H2
Catalysis and Catalysts - Kinetics
Kinetic coupling between catalytic cycleseffect on selectivity
Hydrogenation: butyne -> butene -> butane A1 A2 A3
butyne and butene compete for the same sitesbut: K1 >> K2 resulting high selectivity for butene (desired) possibleeven when k2 > k1
since:22
112,1 Kk
KkS
Meyer and Burwell (JACS 85(1963)2877) mol%:2-butyne 22.0cis-2-butene 77.2trans-2-butene 0.71-butene 0.0butane 0.1
Catalysis and Catalysts - Kinetics
Kinetic coupling between catalytic cycleseffect on selectivity
Bifunctional catalysis: Reforming
Isomerization n-pentane: n-C5 -> i-C5
Pt-function: n-C5 -> n-C5=
surface diffusionAcid function: n-C5= -> i-C5=
surface diffusionPt-function: i-C5= -> i-C5
Catalytic cycles on different catalysts
Affect selectivity:• modify surface (change adsorption properties)• modify fluid phase (change adsorption properties)
benzene hydrogenation M. Soede
low concentrationclose proximity
Catalysis and Catalysts - Kinetics
Competitive adsorption Selective hydrogenation aromaticsCompetitive adsorption
Selective hydrogenation aromatics
S.Toppinen,Thesis 1996S.Toppinen,Thesis 1996
0 2 4 6 8 10
space time / min.g.ml-1
0
5
10
15
20
25
30
conc
entr
atio
n / w
t.%
CH3
CH3
CH3
CH2
CH3
CH3
H3C CH3
Ni-alumina trilobe catalyst3 mm particles40 bar H2
125oCsemi-batch reactor
Ni-alumina trilobe catalyst3 mm particles40 bar H2
125oCsemi-batch reactor
•Consecutive conversion behaviour•rate constants ~ similar•adsorption constants decrease
•Consecutive conversion behaviour•rate constants ~ similar•adsorption constants decrease
Propose a rate expression to account for this effectPropose a rate expression to account for this effect
Catalysis and Catalysts - Kinetics
Partial benzene hydrogenationPartial benzene hydrogenation
Ru-catalyst - clusters of crystallites Slurry reaction, elevated pressures Water-salt addition increases selectivity
+ + 2 H2 H2
RuSalt-water
Adsorption / Desorption properties affectedAdsorption / Desorption properties affected
Catalysis and Catalysts - Kinetics
Dual site models:A + B C
A + * A*
B + * B*
A* + B* C* + *
C* C + *
(r.d.s.)
2
421
213
/1
/
KppKpK
KpppKKNskr
CBA
eqCBAT
Catalysis and Catalysts - Kinetics
Surface occupanciesSurface occupancies
Empty sites:
Occupied by A:
Occupied by B:
B 3
B1 A B 3
/
1 /
p K
K p p K
1 A
A1 A B 31 /
K p
K p p K
*1 A B 3
1
1 /K p p K
Catalysis and Catalysts - Kinetics
Dual site models, contd.
*3333 CBAT kkNsrrr
Number of neighbouring sites (here: 6)